\contentsline {section}{\numberline {1}Abstract}{2}{section.1}
\contentsline {section}{\numberline {2}Introduction}{4}{section.2}
\contentsline {section}{\numberline {3}Background}{4}{section.3}
\contentsline {subsection}{\numberline {3.1}Euclidean Algorithm}{4}{subsection.3.1}
\contentsline {subsection}{\numberline {3.2}Extended Euclidean Algorithm}{4}{subsection.3.2}
\contentsline {subsection}{\numberline {3.3}Modular Multiplicative Inverses}{5}{subsection.3.3}
\contentsline {section}{\numberline {4}Symmetric Key Cryptography}{5}{section.4}
\contentsline {subsection}{\numberline {4.1}Example}{5}{subsection.4.1}
\contentsline {section}{\numberline {5}Public Key Cryptography}{6}{section.5}
\contentsline {subsection}{\numberline {5.1}Public key in Comparison to Symmetric-key}{6}{subsection.5.1}
\contentsline {subsection}{\numberline {5.2}The Discrete Logarithm Problem}{6}{subsection.5.2}
\contentsline {subsubsection}{\numberline {5.2.1}Shanks' Baby-Step Giant-Step approach}{7}{subsubsection.5.2.1}
\contentsline {subsubsection}{\numberline {5.2.2}Pollard's $\rho $ and $\lambda $ method}{8}{subsubsection.5.2.2}
\contentsline {subsubsection}{\numberline {5.2.3}Pohlig-Hellman}{8}{subsubsection.5.2.3}
\contentsline {subsection}{\numberline {5.3}Elliptic Curves}{8}{subsection.5.3}
\contentsline {subsection}{\numberline {5.4}Diffie-Hellman Problem}{8}{subsection.5.4}
\contentsline {subsection}{\numberline {5.5}ElGamal Encryption}{8}{subsection.5.5}
\contentsline {subsection}{\numberline {5.6}RSA Encryption}{8}{subsection.5.6}
\contentsline {section}{\numberline {6}Discussion of the Results}{8}{section.6}
\contentsline {section}{\numberline {7}Conclusion}{8}{section.7}
\contentsline {section}{\numberline {A}Bibliography}{9}{appendix.A}
